The Eagles (10-7, 4-0 Atlantic Sun Conference) shot 50.8 percent from the field and scored 20 points off turnovers to North Florida's 11. Chase Fieler and Bernard Thompson each scored 12 points, capping four starters in double figures.
After trailing by six early in the second half, FGCU surged ahead as Jones converted a three-point play to ignite an 11-1 run and put the Eagles up 71-62 with 4:42 remaining. North Florida stormed back to pull within one with 22 seconds left, but FGCU finished 5 of 6 from the free-throw line to ice the game.
Washington State's trio of Josh Hawkinson, Conor Clifford and Ike Iroegbu have withdrawn from the NBA draft and will play their senior season with the Cougars.
Gonzaga center Przemek Karnowski, who missed most of last season with a back injury, says he is returning for another year.
Wisconsin forward Nigel Hayes has withdrawn from the NBA draft and will return to the Badgers for his senior season.